论文标题
使用张量火车学习Feynman图
Learning Feynman Diagrams with Tensor Trains
论文作者
论文摘要
我们使用张量化网络技术以非常高的精度来获得量子多体问题的高阶扰动图的扩展。该方法基于张量列的所有Feynman图的总和的张量表示，该表示的总和是通过张量交叉插值算法以受控且准确的方式获得的。在存在任何任意时间相互作用的情况下，它产生了物理量的全职演变。在实时的非平衡schwinger-keldysh形式主义中，我们对安德森量子杂质问题的基准测试表明，该技术取代了图形量子量的蒙特卡洛，按精度和速度的数量级，收敛速度为$ 1/n^2 $或较固定的$ 1/n^2 $，n是功能评估的数量。该方法还起着参数状态的作用，其特征在于高维度的强烈振荡积分，这些积分在量子蒙特卡罗中遇到了灾难性的标志问题。最后，我们还提出了两项探索性研究，表明该技术将其推广到更复杂的情况：双量子点和一个嵌入二维晶格中的单个杂质。
We use tensor network techniques to obtain high order perturbative diagrammatic expansions for the quantum many-body problem at very high precision. The approach is based on a tensor train parsimonious representation of the sum of all Feynman diagrams, obtained in a controlled and accurate way with the tensor cross interpolation algorithm. It yields the full time evolution of physical quantities in the presence of any arbitrary time dependent interaction. Our benchmarks on the Anderson quantum impurity problem, within the real time non-equilibrium Schwinger-Keldysh formalism, demonstrate that this technique supersedes diagrammatic Quantum Monte Carlo by orders of magnitude in precision and speed, with convergence rates $1/N^2$ or faster, where N is the number of function evaluations. The method also works in parameter regimes characterized by strongly oscillatory integrals in high dimension, which suffer from a catastrophic sign problem in Quantum Monte-Carlo. Finally, we also present two exploratory studies showing that the technique generalizes to more complex situations: a double quantum dot and a single impurity embedded in a two dimensional lattice.
